In this work we present the analysis of the dynamic of the expansion of Al Plasma produced by Nd:YAG laser (1064 nm, 500mJ, 9 ms, 10 Hz) in vacuum. To study the Coulomb interaction between the particles of the initial states of the plasma expansion, we use the one dimensional Particle-in-Cell method (PIC) and finite difference method. We considered an ideal model, that is, we assume that the plasma is in a local thermal equilibrium, the ablated particles have a fixed temperature and a constant evaporation flux (J) from the aluminium surface. To obtain more accurate results we use high computing exploiting the parallelization of this kind of algorithms. The mean velocity and particles densities are determined for different times of the expansion.